Nanoparticles are ubiquitous and by far the most abundant particle-like entities in natural environments on Earth and are widespread across many applications associated with human activities. There are many types of naturally occurring nanoparticles and man-made (engineered) nanoparticles. Nanoparticles occur in air, aquatic environments, rain water, drinking water, bio-fluids, pharmaceuticals, drug delivery and therapeutic products, and a broad range of many industrial products. Nanoparticles usually occur within poly-disperse assemblages, which are characterized by co-occurrence of differently-sized particles.
Given the widespread usage of nanoparticles, the ability to control and accurately characterize their properties may be useful to many applications. Conventional methods for measuring nanoparticle properties may be inaccurate for poly-disperse samples of mixed nanoparticle sizes, which are common in many applications. Some of these conventional approaches make measurements on an ensemble of a large number of nanoparticles within a sample. Because the light scattered from all nanoparticles is measured simultaneously, it may be difficult to resolve the nanoparticles into their constituent sizes when there is a range of particle sizes. Other approaches fail to account for the large differences in the intensity of scattered light produced by differently-sized nanoparticles across the range of nanoparticle sizes. In these approaches, the low scattering signals from small nanoparticles may be undetected, or the high scattering signals from larger nanoparticles can obscure the signals from smaller nanoparticles. And in yet other approaches, the measurements fail to account for the growth rate or dissolution rate of the particles, such that a snap-shot of a size distribution could be inaccurate a few moments later. As a result of these deficiencies, the concentration of nanoparticles of any given size, and hence the entire size distribution, can be subject to unknown error.
These methods of detecting nanoparticles are commonly referred as dark field microscopy. An instrument setup 10 is shown in FIGS. 1A and 1B to perform such an analysis. The setup typically comprises: a light source 15 that produces light beam 20 that passes through cylindrical lens and an optical objective 25 that form a light sheet 30, which is directed at a small cell (cuvette) 35. The cuvette 35 contains the nanoparticles in a colloid made out of a diluent, some of them being observed within the investigated volume 38. The nanoparticles in the investigative volume 38 scatter light 40 that is directed through a focusing optical objective 45 (which may also include magnifying optical objectives—i.e., a microscope), producing a focused light beam 50 onto a sensor (e.g., camera) 55. A processor 60 may be connected to the sensor 55 and the light source 15 to control them. The setup 10 enables illumination of any liquid with a precisely-formed, narrow light sheet and observation of scattered light from the nanoparticles, usually at a 90-degree angle relative to the light sheet plane. In other words, the direction of observation is perpendicular to the direction of the plane of illumination.
Different sized particles can be visualized owing to the camera capturing reflected light images from the particles, with such images having different intensities (various brightness of pixels comprising an image) based on the size of particles and their composition (refractive index different than refractive index of a diluent). By tracking images of scattered light on subsequent frames of recorded videos and using theory of Brownian motion (Einstein's equation), one can determine size of each observed particle individually (this is usually called Nanoparticle Tracking Analysis or NTA). Since one can count and size all observed particles, in principle particle size distribution (PSD) can be also calculated accurately. Typically, to obtain such distribution one bins sizes of particles, i.e. adds number of all particles that have sizes within a certain range of diameters and places them in separate bins corresponding to this range of diameters. To obtain PSD, the number of particles in each bin is divided by the corresponding bin width and by the investigated volume.
The problem with this method is the non-uniformity of light intensity of the light sheet that is being used to visualize particles for tracking and counting. The area observed by the camera is easily calibrated by using microscales to find exact calibration constant, i.e. number of length units per camera pixel, as shown in FIG. 2. An ideal light sheet would have a “top hat” light intensity characteristic 65—i.e., there will be a sharp border between illuminated and dark regions (volumes) of a sample as shown in FIG. 3. However, optical devices used to produce light sheets like lasers, lens and objectives, typically generate Gaussian-like profiles 70 of light intensity—see FIG. 3 showing “top hat” distribution 65 as compared to a Gaussian distribution (same intensity or area under both curves). Depending on light scattering cross section for a given particle material in a given diluent and the camera sensitivity (quantum efficiency), the effective light sheet thickness, and thus investigated volume, can vary considerably (particles being closer to the edge of light sheet receive less light for scattering and thus possibly are not being detected by the apparatus). This variable investigative volume will highly influence the determination of PSD or concentration of particles in a colloid unless it is properly accounted for.
Therefore, a need exists for properly calibrating the investigated volume for different types and different sizes of particles. This size/type dependent investigated volume can then be used to arrive at a more precise determination of PSD or particle concentration for any colloid.